Derivative formulae for heat semigroups are used to give gradient estimates for harmonic functions on regular domains in Riemannian manifolds. This probabilistic method provides an alternative to coupling techniques, as introduced by Cranston, and allows us to improve some known estimates. We discus
Boundary Behavior of Harmonic Functions on Manifolds
β Scribed by Jiecheng Chen
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 161 KB
- Volume
- 267
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we mainly set up a kind of representation theorem of harmonic functions on manifolds with Ricci curvature bounded below and study non-tangential limits of harmonic functions.  2002 Elsevier Science (USA)
π SIMILAR VOLUMES
In this paper we derive some geometric formulas for the quotient of the zeta functional determinants for certain elliptic boundary value problems on Riemannian 3 and 4-manifolds with smooth boundary. 1997 Academic Press ## 1. Introduction Let (M, g) denote a smooth compact Riemannian manifold wit
In this paper we show W 2, 2 -compactness of isospectral set within a subclass of conformal metrics, and discuss extremal properties of the zeta functional determinants, for certain elliptic boundary value problems on 4-manifolds with smooth boundary. To do so we establish some sharp Sobolev trace i
## Abstract A harmonic function defined in a cone and vanishing on the boundary is expanded into an infinite sum of certain fundamental harmonic functions. The growth conditions under which it is reduced to a finite sum of them are discussed.
A growth lemma for certain discrete symmetric Laplacians defined on a lattice Z d Ξ΄ = Ξ΄Z d β R d with spacing Ξ΄ is proved. The lemma implies a De Giorgi theorem, that the harmonic functions for these Laplacians are equi-HΓΆlder continuous, Ξ΄ β 0. These results are then applied to establish regularity